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A059555 Beatty sequence for 1 + gamma A001620. 4
1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 89, 91, 93, 94, 96, 97, 99, 100, 102, 104, 105, 107, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let r = gamma (the Euler constant, 0.5772...). When {k*r, k >= 1} is jointly ranked with the positive integers, A059555(n) is the position of n and A059556(n) is the position of n*r. - Clark Kimberling, Oct 21 2014
LINKS
Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no. 4, 335-345.
Eric Weisstein's World of Mathematics, Beatty Sequence.
FORMULA
a(n) = n + A038128(n).
MAPLE
A001620 := proc(n)
floor((1+gamma)*n) ;
end proc:
seq(A001620(n), n=1..50) ; # R. J. Mathar, Nov 11 2011
MATHEMATICA
t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]
Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]] (* A059556 *)
Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)
(* Clark Kimberling, Oct 21 2014 *)
PROG
(PARI) { default(realprecision, 100); b=1 + Euler; for (n = 1, 2000, write("b059555.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009
(Magma) R:=RealField(100); [Floor((1+EulerGamma(R))*n): n in [1..100]]; // G. C. Greubel, Aug 27 2018
CROSSREFS
Beatty complement is A059556.
Sequence in context: A247779 A243989 A248521 * A186539 A054385 A284773
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Jan 22 2001
STATUS
approved

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Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)